Question: Reduce to lowest terms: $ \dfrac{5}{8} \div - \dfrac{4}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{9}$ is $- \dfrac{9}{4}$ Therefore: $ \dfrac{5}{8} \div - \dfrac{4}{9} = \dfrac{5}{8} \times - \dfrac{9}{4} $ $ \phantom{ \dfrac{5}{8} \times - \dfrac{9}{4}} = \dfrac{5 \times -9}{8 \times 4} $ $ \phantom{ \dfrac{5}{8} \times - \dfrac{9}{4}} = \dfrac{-45}{32} $